On Sasaki-Einstein manifolds in dimension five

TL;DR

This paper establishes the existence of Sasaki-Einstein metrics on specific simply connected 5-manifolds with non-trivial torsion, revealing multiple deformation classes and expanding the known landscape of such geometric structures.

Contribution

It proves the existence of Sasaki-Einstein metrics on new classes of 5-manifolds with torsion, and demonstrates the presence of infinitely many deformation classes.

Findings

Existence of Sasaki-Einstein metrics on certain 5-manifolds

Presence of infinitely many deformation classes on some manifolds

Manifolds with non-trivial torsion admit these structures

Abstract

We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes. On several of these we show that there are a countable infinity of deformation classes of Sasaki-Einstein structures.